Octet baryon magnetic moments at next-to-next-to-leading order in covariant chiral perturbation theory

TL;DR

This paper calculates octet baryon magnetic moments using covariant chiral perturbation theory up to NNLO, proposing methods to determine low-energy constants and comparing different formulations to understand convergence with lattice data.

Contribution

It introduces two strategies to fix low-energy constants at NNLO and compares three formulations of baryon chiral perturbation theory using lattice QCD data.

Findings

Proposed methods to determine low-energy constants at NNLO.

Compared different chiral perturbation theory formulations.

Highlighted the importance of precise lattice data for convergence understanding.

Abstract

We calculate the octet baryon magnetic moments in covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme up to next-to-next-to-leading order. At this order, there are nine low-energy constants, which cannot be uniquely determined by the seven experimental data alone. We propose two strategies to circumvent this problem. First, we assume that chiral perturbation theory has a certain convergence rate and use this as one additional constraint to fix the low-energy constants by fitting to the experimental data. Second, we fit to lattice QCD simulations to determine the low-energy constants. We then compare the resulting predictions of the light and strange quark mass dependence of the octet baryon magnetic moments by the three mostly studied formulations of baryon chiral perturbation theory, namely, the extended-on-mass-shell, the infrared, and the heavy baryon approach. It is shown that once more precise lattice data become available, one will learn more about the convergence pattern of baryon chiral perturbation theory.